Question

The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

Length (in mm)	Number of leaves
118−126	3
127–135	5
136−144	9
145–153	12
154–162	5
163–171	4
172–180	2

Find the mean length of the leaves.

Answer 1

Length (in mm)	Number of leaves (f)	CI	Mid x	d	fd
118−126	3	117.5 − 126.5	122	-27	-81
127−135	5	126.5 − 135.5	131	-18	-90
136−144	9	135.5 − 144.5	140	-9	-81
145−153	12	144.5 − 153.5	a = 149	0	0
154−162	5	153.5 − 162.5	158	9	45
163−171	4	162.5 − 171.5	167	18	72
172−180	2	171.5 − 180.5	176	27	54

Mean = `"a" + (sum"fd")/(sum"f")` 

= `149 + (-8)/40`

= 149 - 2.025

= 146.975

Average length of the leaves =  146.975.